Sinkhorn divergence [1]} is another measure of dissimilarity related to Wasserstein distance. It is obtained through adding an entropic regularization
term to the Kantorovich formulation of optimal transport problem. It
can hence be viewed as a regularized Wasserstein distance with
desirable convexity and regularity properties.
A main advantage of Sinkhorn divergence over Wasserstein
distance lies in its computability by an iterative algorithm
known as Sinkhorn's matrix scaling algorithm [2]}, where
each iteration involves two matrix-vector products.
Consequently, Sinkhorn divergence may serve as a feasible alternative to classical
Waaserstein distance, particularly when probability measures are
supported on multi-dimensional spaces in \({\mathbb {R}}^d\)  with \(d \ge 2\) .
